Seven different objects must be divided among three people. In how many ways can this be done if one or two of them must get no objects?
36
84
180
381
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Two variants of the CAT paper are to be given to 12 students. In how many ways can the students be placed in two rows of six each so that there should be no identical variants side by side and that the students sitting one behind the other should have the same variant. Find the number of ways this can be done
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2
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In how many ways a committee, consisting of 5 men and 6 women can be formed from 8 men and 10 women?
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3
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There are 8 orators A, B, C, D, E, F, G, and H. In how many ways can the arrangements be made so that A always comes before B and B always comes before C.
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4
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How many words, with or without meaning, can be formed using all letters of the word EQUATION using each letter exactly once?
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5
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There are three rooms in a motel: one single, one double, and one for four persons. How many ways are there to house seven persons in these rooms?
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6
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A basketball team of 5 players is to be selected from a group of 10 men and 8 women players. A volley ball team of 6 players is to be selected from a group of 8 men and 7 women players. Find the difference in the number of ways in which both the teams are selected, given that each team has only 2 female players.
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7
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In how many ways the letters of the word “UNDERDOG” can be arranged such that the first and last letters are same and no two vowels are together?
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8
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What is the probability of getting at least one six in a single throw of three unbiased dice?s
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9
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Find the number of ways in which mixed double tennis game can be arranged amongst 9 married couples if no husband and wife play in the same game
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10
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A box contains 5 green, 4 yellow and 3 white marbles. three marbles are drawn at random. What is the probability that all they are not of the same colour?
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